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(Warning: Do not try to simplify the mathematical expression above, or it won't work if you try it.)

Note by Michael Mendrin
2 years, 5 months ago

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Michael Mendrin · 2 years ago

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@Michael Mendrin I either need to sleep or the end is near... John Muradeli · 2 years ago

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@John Muradeli Oh gawd, that wasn't supposed to be there. I was checking out how to post GIFs, for a new problem. Here's the new problem: Shortest Distance On Tesseract Michael Mendrin · 2 years ago

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You've been recently posting some really cool problems. Are they original?

Also, that's a very interesting way to generate prime numbers... Daniel Liu · 2 years, 5 months ago

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@Daniel Liu I am also now keeping my problems together in one place where I can find them

Michael Mendrin Problems

In looking them over, "That Other Dodecahedron" was a problem posed by somebody I know, and I was able to prove it in the general case of [any irregular] pentagons of equal sides.. So, that one is not mine. "This Is Just Arithmetic!" is an old chestnut, not mine. "Equilateral Triangle Dissection" was something a proof was asked for by another I know, I adapted it for Brilliant. The rest are products of having plenty of time on my hands, kind of like my little works of art. Including that formula you see up there, which was adapted from another prime number generator.

I see that you're a pretty prolific contributor to Brilliant. I always wonder how you guys (including Calvin Lin) find the time or get them out so fast. Michael Mendrin · 2 years, 5 months ago

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@Michael Mendrin I have created a lot of my problems for the past 5 years, and many were inspired by existing problems that I like. Only about 25% of my problems were created by myself. Steven Zheng · 2 years, 5 months ago

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@Steven Zheng But when did you post so many problems?? Anuj Shikarkhane · 2 years, 5 months ago

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@Steven Zheng Well, I do have a nice backlog of problems posted elsewhere by others that I know, but I'm finding out that they're also posting their own problems here! So, out of respect, I'll keep my hands of those. Michael Mendrin · 2 years, 5 months ago

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@Michael Mendrin Who are these people? I might want to follow them. Steven Zheng · 2 years, 5 months ago

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@Steven Zheng They've come and gone, but Brian Charlesworth is still around. Vikram Pandya is the one that told me to try Brilliant, but these days I think he's too busy being a banker. Both have posted excellent problems. Michael Mendrin · 2 years, 5 months ago

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@Daniel Liu May I refer you to the Katie-Cody Prime Number Formula? Cody Johnson · 2 years, 5 months ago

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@Cody Johnson That's certainly one of the tidier prime number formulas that I've seen that uses floor and ceiling functions. On a lark, I had decided to fool around and use mathematical expressions that take place of floor and ceiling functions, and created this picturesque formula up on top. Michael Mendrin · 2 years, 5 months ago

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Do you like carrots? Agnishom Chattopadhyay · 1 year, 3 months ago

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@Agnishom Chattopadhyay You ask this to all folks! You asked me this! Kishore S Shenoy · 1 year, 3 months ago

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@Kishore S Shenoy Kishore, I think Agnishom is planning to corner the market on carrots. Michael Mendrin · 1 year, 3 months ago

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@Michael Mendrin LoL! Hehe wildman, you are hilarious!! Kishore S Shenoy · 1 year, 3 months ago

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@Agnishom Chattopadhyay I eat carrots, yes. Cooked and uncooked. Michael Mendrin · 1 year, 3 months ago

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Comment deleted Oct 18, 2015

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@Maria Kozlowska Maria, if you upset me, it's because you keep disappearing! Otherwise, why would I feel upset? I still enjoy good pasta.

Edit: Disappeared again! Michael Mendrin · 1 year, 3 months ago

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@Michael Mendrin What! What is all this! Kishore S Shenoy · 1 year, 3 months ago

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@Kishore S Shenoy oh go ask Maria Michael Mendrin · 1 year, 3 months ago

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Hi Mike! Kishore S Shenoy · 1 year, 3 months ago

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@Kishore S Shenoy Hey Michael Mendrin · 1 year, 3 months ago

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Comment deleted Oct 19, 2015

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@John Muradeli I think maybe you're having a major burnout? The thing is, if you're already out of school and working, you can just quit and go off in a different direction until you figure out what you really want to do (believe me, I know what that's like). But when you're still in school... well, I've often heard that sometimes it's best that after high school, one takes a year-long break to first get a good grip of what are the priorities. What do you really want?

When I am up in the mountains, I never get lost. I am merely only momentarily confused as to where I am. So far, nobody's ever have to come and find me. Michael Mendrin · 1 year, 3 months ago

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Sir, recently I came upon a question by Alex Segesta --

Find the digit sum of \( 2222...222^2 \). There are \( 2014 \) 2s.

I had to resort to writing a computer code to solve it.What I want to ask sir is that is there a way to solve this question using only mathematics.

Thanks for the same Azhaghu Roopesh M · 2 years ago

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@Azhaghu Roopesh M Wiki Megh Choksi · 2 years ago

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@Megh Choksi Thank you Megh, I'll need some time to read about it so I better get going . Azhaghu Roopesh M · 2 years ago

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please solve: https://brilliant.org/problems/can-you-solve-it-9/?group=j4P7dyAoNhAb&ref_id=568173 Visakh Radhakrishnan · 2 years ago

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Hello Sir, can you help me - With this problem 14 solver but no solution.

Sir can I ask - are you a mathematician or a physicist or a professor in a college? Megh Choksi · 2 years ago

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@Megh Choksi Uh, I'm not a professional mathematician, physicist, or a professor. I haven't ever published any papers. But don't let that discourage you, huh? Michael Mendrin · 2 years ago

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@Michael Mendrin No , thanks for replying Megh Choksi · 2 years ago

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Sorry for troubling you, but can u help me out with this one Aneesh Kundu · 2 years, 3 months ago

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Michael, I am actually a bit more curious about Quatum theory. I just want to ask a simple question, that Quatum entanglement says there should be opposite versions of same things. Let's come to Schrödinger's cat.Suppose there are three boxes A, B, and C and three persons X, Y and Z and each of them is observing two boxes not even knowing that there exists a third box. X looks at A and B, Y at B and C and Z at C and A . So, here's the contradiction, X should find one cat alive and one dead, so let us assume A to be alive and B to be dead. Y should also find one cat alive and one dead, so he will observe B dead and C alive. But Z would find both A and C alive , so how could this be possible? Utkarsh Dwivedi · 2 years, 4 months ago

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@Utkarsh Dwivedi It works like this. Let's imagine we're able to prepare 3 quantum entangled cats, each that can have any 1 of 3 "states" or, "colors" or "flavors", like Red, Green, or Blue, but that no 2 can have the same color. Let's further imagine that we prepare many, many such triples of quantum entangled cats. When any one observer, say, X, looks into boxes A and B for each successive prepared entangled cats, what he will see is a seemingly normal random sequence of pairs of colors that are not alike. Other observers Y and Z report the same thing, regardless of when and where they've made their observations. But when their collected data are compared, then it can be seen that all 3 cats are always in different colors, no matter how much any one of them try to influence the outcome of their own observation.

The problem with your proposal is that it's not quite possible to prepare 3 quantum entangled cats, each that have any 1 of TWO states, and yet no 2 can have the same state! Then it doesn't matter how many observers there are or how the cats are observed, obviously we can't ever find out out that of the 3 cats, 2 of them aren't dead, AND two of them aren't alive! Quantum stuff can be pretty weird, but not that weird.

It might seem obvious that when entangled pairs of particles are prepared, they could "already" be in their states, just waiting to be observed. But more sophisticated experiments have shown this not to be true, i.e., for each of the entangled pairs of particles, it's still like being Schrodinger's Cat, its state truly being random until actually observed. Michael Mendrin · 2 years, 4 months ago

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@Michael Mendrin Also try for four Utkarsh Dwivedi · 2 years, 4 months ago

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@Michael Mendrin But, good to say that, if ever ever a scientist or a physicist, prepares three models of, let's not take the case of Schrödinger's cat as they are macroscopic, let's take example of real " Quatum Stuff ", according to Quatum entanglement when two particles are observed which are not previously observed, then one of them would rotate anticlockwise and one clockwise. Fair enough. But if a scientist or a physicist who is as mad as me , though I am not a scientist or a physicist, conducts this experiment with three observers, and this case too there are only two states but three observers what will each one of them observe, if one of them observes two anticlockwise or clockwise rotating particles then this could be used as a contradiction for quantum entanglement. Utkarsh Dwivedi · 2 years, 4 months ago

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Hi sir micheal....i was wondering what this image is stating?Could you explain it a bit?? Ankit Vijay · 2 years, 4 months ago

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@Ankit Vijay It's a mathematical formula that returns the nth prime number, given n, without using any floor or ceiling functions. if you look elsewhere on this messageboard, there's discussion on this subject. It looks pretty, but I'm not expecting any Fields Prize. Michael Mendrin · 2 years, 4 months ago

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Ever tried to prove the Reimann Hypothesis? Danny Kills · 2 years, 5 months ago

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@Danny Kills Oh, god, no, you must think I'm a genius or something. Michael Mendrin · 2 years, 4 months ago

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@Michael Mendrin You are. John Muradeli · 2 years, 3 months ago

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@John Muradeli Agreed... Either that, or a reasonable facsimile. :) I'm curious, though, what would qualify someone to be considered a genius in Michael's eyes, and whether or not he has encountered them in any discipline. I've known prodigies and brilliant minds, but no one I would consider a genius. Thoughts, @Michael Mendrin ?

P.S.. Would gianlino from our Y!A days qualify? Brian Charlesworth · 2 years, 3 months ago

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@Brian Charlesworth Yes, gianlino qualifies. I remember him solving one of the hardest @@@@ problems there is on Y!A, and I just wonder if I should post it here and see if anybody can do it. Michael Mendrin · 2 years, 3 months ago

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@Michael Mendrin Are you on quora ? Or project euler? Thaddeus Abiy · 2 years ago

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@Thaddeus Abiy I have an Quora account, but I haven't contributed anything. Project Euler is something I hadn't heard about until now. But I find these kinds of things a bit too distracting for me, it's hard for me to find the time to do my own thinking. Michael Mendrin · 2 years ago

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@Michael Mendrin The style of Project Euler problems is actually very similar to your problems especially the latter ones. I tried searching for you on Quora but couldnt find you. Do you go by a different name there? Thaddeus Abiy · 2 years ago

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@Thaddeus Abiy I think in Quora, the moniker is "Michael Scythian", which is my Facebook name? I can't keep track of this, you know? In Yahoo Answers, I went by the name "Scythian1950", I had frequented Y!A until it just fell apart, and I moved over to Brilliant.

In fact, it's really hard for me to explain what is it that I'd rather spend my time thinking about. It has to do with the nature of mathematics and how it impacts physics--mainly how advances in theoretical physics depends on innovation in mathematics. And it can't wait for "rigor".

Also, that reminds me, my Facebook avatar is a really cute geometrical problem by itself, too bad that I can't figure out how to re-frame it to fit the Brilliant format. Wikipedia says that there are only 8 convex deltahedrons, i.e., convex polyhedra with identical equilateral triangle faces. In fact, there's at least one more. But how can I make that a Briliant problem? I don't know yet. Michael Mendrin · 2 years ago

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@Michael Mendrin Alright! Now I can stalk you on Brilliant AND Yahoo! John Muradeli · 2 years ago

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@John Muradeli Good luck with that, because I don't hardly go to Y!A any more, except to rummage through my old posts there for new problems here. I can be so lazy. Michael Mendrin · 2 years ago

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@Michael Mendrin Lol jk :)

Plus I think we can agree Brilliant is one of the awesomest if not THE awesomest math and physics conglomerate EVER! John Muradeli · 2 years ago

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@John Muradeli It would be more awesome to me if I could find it easier to get a good, roiling dialogue going on interesting topics. That's what you're so good at, keep up the crazy work. I get bored to tears with pedantic mathematical precision, too much of the time I feel like I'm in law school. Michael Mendrin · 2 years ago

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@Michael Mendrin Oh geez thanks I take that as a compliment!

[NOTE: If you're not interested in politics, disregard this post.]

Well how about this: I am flying to San Francisco this Thursday for the annual Harvard Model Congress debates. I have been assigned the role of Intelligence and I am representing the Democratic Representative of Rhode Island's 2nd Congressional District, James Langevin.

If you haven't heard of it I suggest you check it out. But basically the purpose of HMC is to debate with (for most part) intelligent students from all over the world about the US domestic and foreign policies. This serves to help students grow socially and intellectually. The way it works is that people gather, and after countless introductory and preparatory procedures, get to present the bills that they've written and possibly have revised with the help of other delegates. Then the debates hold and delegates vote on the bill.

However, if a bill is strongly agreed upon, and if Harvard representatives feel that the bill could become a law, it is then sent to the government for further looks, and can be passed to become an act! The designer of such a bill receives a National Award, along with, I believe, monetary prize.

Isn't that awesome?

My issue is the Military Use of Drones. I have done quite some research and am in the process of crafting a bill. If you're interested I could make a note with my bill and we could have a look.

Cheers! John Muradeli · 2 years ago

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@John Muradeli I'm impressed, John. This sounds like a fascinating and worthwhile endeavor. As I mentioned to Michael, politics is another addiction of mine, probably starting around the time of the Iran hostage crisis back in the late 70's. As for drones, one of my biggest concerns is the possibility of these things being hacked; for this reason alone I would argue that they should not be armed with lethal hardware. Your ideas regarding non-lethal components have great merit, however. Brian Charlesworth · 2 years ago

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@Brian Charlesworth Politics is a truly wonderful subject. I prefer it over math any day. The key is to remain as objective as possible, and you can have a blast.

In fact, politics often involves more critical thinking than math. There is no Wolfram|Alpha for politics, now is there?

Besides, politics is far more applicable and useful in real life. It involves so many critical skills... Leadership, rhetoric, management, writing, etc. etc...

And to be honest, the more social science you know, the less you begin to care about the typical "genius" and "talented" people, and the more you begin to see the world through the eyes of a problem-solver. Of course this does not include the exceptional Einstein, Shakespeare, or anyone as such, but I mean that those kids that can solve rubiks cube in 5 seconds or solve differential equations at the age of 4 - they simply become... well... would take long to type... and oh darn here I am again steaming my manifestae (oh yeah I did). Better get back to HW! Got 4AP homeworks and a Bill to craft!

Laters! John Muradeli · 2 years ago

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@John Muradeli Beautifully said; my sentiments exactly. Cheers! Brian Charlesworth · 2 years ago

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@John Muradeli Well, politics for me is kind of like a recurring disease, like shingles or something, where I can get involved for a while, like during presidential election years, and then I forget all about it. Drones, yeah, that is a weighty subject, lots of pros and cons---is America becoming a Skynet, raining death and destruction from airborne robots, and is that a good thing? Yes and no. It's a complicated subject. It's not a lot different from the controversy over the dropping of the A-bomb on Hiroshima and Nagasaki, many still say it was an atrocity, but many others say that it avoided implementation of Operation Downfall, the invasion of mainland Japan, thus saving many millions of lives. I agree that military use of drones is something that should be highly regulated, especially when there is no declared war, so the question becomes, when are drones ever appropriate, and what should be the rules of engagement? Michael Mendrin · 2 years ago

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@Michael Mendrin I don't get it am I the only one with this idea? Here, you can have the preamble of my bill, and a little summary on its contents:


Be it hereby enacted by the US Senate:

\[\large{\text{Drone Neutralization Act}}\]

Preamble

The United States House resolves to reduce unintended casualties due to the military use of drones in the War on Terror by funding research on development of precise, non-lethal weaponry, and the incorporation of such weaponry into the drone arsenal.

Contents

Suppressive bullets; mass stun projectiles; tranquilizer sniper guns, ...

Sample explanation of content:

Tranquilizer sniper guns:

Mounted on drones, tranquilizer technologies will effectively neutralize human targets, rendering them incapable of self-defense or escape. Utilizes great precision and minimizes unintended casualties. Can be modified with noise suppressors to evade enemy detection and retain stealth.


This bill aims to resolve the issues from conservative and liberal perspectives, and there are many.

What do you think? Like the ideas so far? I'm still crafting the bill - need to finish contents and put together enforcement and funding. John Muradeli · 2 years ago

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@John Muradeli One question comes to mind .... How do we know that the military (or any of the private contractors) are not already working on some of these options? Brian Charlesworth · 2 years ago

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@Brian Charlesworth I've researched. A lot. Google and Bing reveal nothing. It could be a secret, of course, but the good part is that if it is, I can still enact it as my own idea. Besides, I doubt they have ALL of the things I've thought up. Laser-guided silent electromagnetic tranquilizer missiles? ;) John Muradeli · 2 years ago

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@John Muradeli Haha. Perhaps you should add a rider to the bill that requires that you be hired as a "creative consultant". Gosh, that's not a scary thought at all, is it?! :) Brian Charlesworth · 2 years ago

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@Michael Mendrin I wouldn't have wanted to be in Truman's shoes on the A-bomb decision; I still go back and forth on that one. Brian Charlesworth · 2 years ago

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@Michael Mendrin Perhaps there could be a "Discussion of the Week" or "Open Problem of the Week" highlighted on the Home page. Submissions could be made to a designated page, shortlisted by a moderator (or two) and then passed along to Calvin et al for the final choice. The "Discussion" wouldn't even have to be mathematical or scientific in nature; perhaps a dose of philosophy or social sciences would be beneficial for creating a more diverse and vibrant Brilliant community. (Politics, although an addiction of mine, could present some unwanted .... ummm ... volatility.) And for the "Open Problem", this wouldn't have to be an actual "official" open problem but just some vexing problem not unlike the ones we posted for our small Y!A community back in the day. (The one option I miss here on Brilliant is the posting of problems that I am unable to solve myself or by searching the web. I've tried posting a couple as notes but they never seem to gain much traction, probably since no points are involved by participating in such a discussion.) Brian Charlesworth · 2 years ago

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@Brian Charlesworth Bad idea.

Two reasons:

  1. Brilliant houses a large pool of heterogeneous individuals from around the globe. The mix of religious, political, and cultural beliefs/values in society/philosophy types of questions could very likely create tensions between people, and perhaps even hostilities. We don't want that. The prime feature of Brilliant is that it focuses on two entirely objective (for most part) subjects: math and science, therefore minimizing possibilities for heated debates that may cause such negative responses.

  2. Considering what's been said, I'll bring a fact to attention that, simply, I believe that majority of Brilliant users are incompetent in social sciences.

That's all I have to say for this matter on this website.

If we want such discussions we can always go to Debate.org or other linkage institutions that will allow for non-math/science exchange of ideas.

Let Brilliant remain brilliant in math and science. :) John Muradeli · 2 years ago

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@John Muradeli You are probably correct in that assessment, (although I don't like selling people short), but we have had some wide-ranging discussions on the notes you have posted and no lives or egos were damaged in the process. :) That said, if we forget about the non-math/science component for the moment, what do you think about the highlighted Discussion/Open Problem of the Week option in general? Brian Charlesworth · 2 years ago

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@Brian Charlesworth This thread about having Open Discussions on a range of topics that don't necessarily have to do with math or science is getting kind of woolly now. My suggestion is that one of us can create a note, much like this messageboard, and let it get buried, so that the discussions in it can be sort of semi-private and less likely to generate political controversy. Do we really want to delve into the merits and demerits of the Quran, right now, regarding how it views apostasy? It's probably best that we avoid that third rail, and we stick to less controversial subjects and leave that to the popular media.

The kind of discussion I personally would be more interested in are "controversial subjects in math and physics", such as, "does mathematical rigor ever have an impact on outcomes in theoretical physics?", but I fear that probably too few people would be interested or have something to say about it. Oh, well, but, nevertheless, I think the idea of buried notes serving as semi-clandestine discussion rooms does interest me. Kind of like the French Salon era, when great political, philosophical, scientific, and mathematical thinkers met regularly to have deep discussions. Michael Mendrin · 2 years ago

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@Michael Mendrin Yes, I suppose the wide-ranging Open Discussion idea is a non-starter. I did read a rather heated discussion on one messageboard regarding the consumption of carrots; I shudder to think about what havoc would be wrought if a third rail subject were broached.

The notion of "semi-clandestine discussion rooms" is appealing, though, but they would probably need at least 8 to 12 (more or less) regular participants to thrive. They could only be "advertised" by stealth, but it could also emerge from a "Field of Thoughts" scenario, i.e., if you build it, they will come. I'm curious to see what "revolutionary" idea John has in mind. Brian Charlesworth · 2 years ago

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@Brian Charlesworth Well, you know, the French Salon thing started a couple of revolutions. Michael Mendrin · 2 years ago

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@Michael Mendrin Indeed, and one good revolution deserves another.

P.S.. I just reshared your Messageboard so that perhaps a few more curious souls might stumble upon these discussions. I hope this was in keeping with the "semi-clandestine" directive. :) Brian Charlesworth · 2 years ago

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@Michael Mendrin The thing about philosophy is, you have questions that may never have definitive answers. And that's the way it's supposed to be - refer to your headline. In addition to it, each different perspective may have a different answer in its own respect. And I think that people do not appreciate philosophy because they think it only raises questions instead of answers - but it's the contrary. Philosophy serves to gives us the cornerstone foundations off of which to build our thoughts and perspectives and applications - not to be the applications themselves. This being said, you can think of politics as applied philosophy - which is what I like about it the most.

Now of course there is much more to be said about "philosophy," it being such a great body of knowledge, but for sake of "open discussions," this should deliver the piece of the pie. And I agree with your

idea - we should do that. But I have something even better when I find time - something that will revolutionize Brilliant.org! You'll see! John Muradeli · 2 years ago

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@John Muradeli I always feel like whistling whenever I see a picture of a graveyard. Anyway, yes, regrettably philosophy is often regarded as a bit of a Dead Parrot, (Monty Python), but that doesn't deter me from trying to revive it. :)

I look forward to your (latest) revolutionary idea. Good luck at the conference, and don't forget to try a Mission burrito while in S.F.. Brian Charlesworth · 2 years ago

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@John Muradeli Speaking of philosophy, what do you guys think about the idea that everyone is selfish. Me and a couple of friends recently had a lengthy argument about this. I was indeed incompetent in the social sciences before I came to the U.S but now it intrigues me. I would love to hear your inputs on this. Thaddeus Abiy · 2 years ago

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@Thaddeus Abiy Being labeled as "selfish" has such negative connotations, but I would argue that selfishness is in fact an important component of one's health, both emotional and physical. If you don't take care of yourself first then your long-term ability to care for others and your community will be compromised. It's a biological instinct, as is empathy, so I believe that it is healthier as a species to acknowledge its role and not try to give guilt-trips to those who commit random acts of selfishness. Of course the trait can be overplayed, as can empathy, but, as in all things, moderation is the key.

Anyway, the short answer is yes, since we're all human beings, we are born to be selfish. The question then becomes, how selfish should we allow ourselves to be? The balance of self-awareness and self-interest with the awareness and well-being of others is dynamic, so perhaps a (fluid) state of enlightened self-interest is the ideal. Brian Charlesworth · 2 years ago

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@Brian Charlesworth Hmm..But is self-interest really selfishness? Is selfishness not just a disregard for others. Why can't self-satisfaction and self-interest be separate from selfishness? If we do not distinguish these terms, don't we run the danger of being able to label any human action as selfish? Thaddeus Abiy · 2 years ago

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@Thaddeus Abiy Yes, as Michael says, definition is key, and I chose to look at the concept of selfishness in a broader sense. "Healthy selfishness" is a common term in psychology literature, implying that there is a spectrum of the trait that goes from the negative aspects we normally associate with the word at one end to enlightened self-interest at the other.

I would also argue that self-interest, although generally distinguished from selfishness as Michael points out, tends to be branded negatively as well. I think that this is unhealthy, both from an individual and societal standpoint, since it leads to a shaming of an essential aspect of the human condition. We're not worker bees, but that is what North Americans have generally become, as opposed to those self-indulgent Europeans, (Sarcasm Alert). And yet which cultures have the happier, healthier citizens? Definitely not the States, (except perhaps the "one percent"). So I chose to interpret selfishness in the way that I did so as to 'move the needle' in the discussion so that, as MIchael points out, we are forced to be more honest with ourselves, both as individuals and as a society.

Having said all this, perhaps it would be beneficial for society to shift away from the selfless/selfish dichotomy to that of rational/irrational, or even more radically take the post-structuralist approach of attempting to eliminate labels and dichotomies altogether, (although trying to sift through the occasional post-structuralist manifesto has only ever resulted in further self-loathing, not to mention a pounding headache, but I digress .....). Brian Charlesworth · 2 years ago

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@Brian Charlesworth As I would always say, "this is a false dichotomy to begin with". Life is way too complicated to be reduced to these kinds of Goofus versus Gallant comic strips:

Goofus Gallant

Goofus Gallant

Michael Mendrin · 2 years ago

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@Michael Mendrin Oh wow, social programming at its finest. I wasn't familiar with the "Highlights for Children" magazine, but I've familiarized myself with it now. I had guessed that this strip was from the 50's, but lo and behold it is from 1980. I'd like to see some satirical magazine do a "Goolant and Galfus" comic strip as a reality check, (probably already done .... hopefully). Thanks for the chuckle. :) Brian Charlesworth · 2 years ago

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@Thaddeus Abiy I'm in your corner, Thaddeus.

Arguments in philosophy almost invariably revolve around words and their exact definitions. Here, it's pretty simple. Selfishness and self-interest aren't quite the same thing. Selfishness implies a disregard for the well being of others, while self-interest doesn't necessarily imply it. Meanwhile, self-satisfaction often has nothing to do with either. To illustrate by examples:

1) I have fresh water, and I refuse to share it with others in the lifeboat with me, while we're all out in the sea under a blazing sun. This is selfishness.

2) I have fresh water, and I bottle it and sell it to others, not because I love mankind but because I want the profits. This is self-interest.

3) I have fresh water, and I am thirsty, and so I have me a gulp of it. This is self-satisfaction.

There are a lot of dimensions to human behavior, some of them actually governed by notions of morality, the source of most of such notions of morality having come to us through biological evolution, not as the product of pure rational thought or even strenuous philosophical discourse. Nevertheless, having these kinds of discussions can be very constructive, if we're able to be totally honest with ourselves and who we really are. And too often, that can be very hard for some to do. Michael Mendrin · 2 years ago

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@Michael Mendrin Yes me and my friends had to finally conclude that the argument essentially boils down to how we define the word selfish. I felt that if it was not defined as precisely as you described in your examples above, there would be no use for the words such as selfless or altruism. I do not however understand what you mean when you say 'product of pure rational thought'. What kind of behavior would we exhibit if we had some sort of morality that stemmed from rational thought?Is this even possible without biological evolution? Why would you even need to reason if there isn't any motivation like survival? Thaddeus Abiy · 2 years ago

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@Thaddeus Abiy Okay, because of the the limited space for a response, I would be guilty of oversimplification for saying such a thing, so let's try to start over somewhere and parse this a bit. As human, we do have a number of built-in ideas of what's right and fair, so that if we see that one person is taking advantage of another, or even perhaps brutalizing him, we automatically wish to correct the situation. We do not first work out all the rational reasons why we should want to do such a thing, nor it is necessarily true that we were taught to feel that way. It's often innate. It's even commonly observed in primate behavior, and it has to do with social structures. in other words, it isn't as simple as "self-survival", our behavior and feelings can be influenced by the fact we're part of a society, and for that reason, we can sometimes be altruistic.

That's not to say that none of our ideas of what's moral comes from careful thought. For a classic example, freedom of speech is now a cherished right, but it didn't come to us so easily, it took quite a few thousands of years of discourse and thinking (and fighting!) to the point where we are today. Does that have anything to do with "survival"? Probably not really, and judging from recent events, you'd almost think it's otherwise. And while it could be argued that our wish to enjoy freedom of speech is a form of selfishness (a viewpoint I'd disagree with), it's very hard to argue that our wish to protect freedom of speech of others is a form of selfishness. I'm not even sure how I'd go about that, given that as assigned argument to present in a formal debate. Michael Mendrin · 2 years ago

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@Thaddeus Abiy I will answer your question a few weeks from now. Before that, consider what Dr. Philosophy (Brian Charlesworth) has said about the topic - especially his point about emotional health.

I'll be back as soon as I can. As for now, I'll put Brilliant in my spam folder because I can't stop coming back to this.

Cheers :) John Muradeli · 2 years ago

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@Brian Charlesworth That's the thing. If CALVIN posted my notes, it would be radically different. Back then it was between me you and Michael. Calvin has 10k followers - TEN THOUSAND! Now imagine the standard deviations for populations for the probability of a heated debate as the numbers increase.... oh yeah.

Besides, our topics weren't THAT political. Imagine if we spoke of specific issues - like the War on Terror itself, or the concept of RELIGION, or ... or... well you get the point. I think it would be radically different then.

But sure, consider the SAT prompts (25 minutes to respond to each)


\[\large{\text{SAT Essay Topics}}\]

Our essay topics have been closely modeled on those in the SAT. You can also do the essays given in the first section of each of the tests in the Official Study Guide.

Each of the topics consists of a prompt and an assignment.


Prompt: "That which we obtain too easily, we esteem too lightly. It is dearness only which gives everything its value." Thomas Paine

Assignment: Do we value only what we struggle for? Plan your response, and then write an essay to explain your views on this issue. Be sure to support your position with specific points and examples. (You may use personal examples or examples from your reading, observations, or, knowledge of subjects such as history, literature, science.)


Prompt: If we are afraid to reveal our lack of knowledge we will not be able to learn. In order to make progress we must admit where we are now. Such an admission of ignorance is not easy. As Thoreau says, “How can we remember our ignorance which our growth requires, when we are using our knowledge all the time?”

Assignment: Does the present system of education encourage us to admit our lack of knowledge, or is there too much pressure to demonstrate the acquisition of knowledge? Plan your response, and then write an essay...


Prompt: “A little inaccuracy saves a world of explanation.” C.E.Ayers

Assignment: Is it always essential to tell the truth, or are there circumstances in which it is better to lie? Plan your response, and then write an essay...


Prompt: Many societies believe that the pursuit of happiness is a fundamental human right. But it is also true that attainment of happiness remains elusive. Perhaps Bertrand Russell had it right when he said, “To be without some of the things you want is an indispensable part of happiness.”

Assignment: What gives us more pleasure and satisfaction: the pursuit of our desires or the attainment of them? Plan your response, and then write an essay...


Prompt: “The price of greatness is responsibility.” Winston Churchill

Assignment: Do we expect too much from our public figures? Plan your response, and then write an essay...


Prompt: “A man should never be ashamed to own he has been in the wrong, which is but saying, in other words, that he is wiser today than he was yesterday.” Alexander Pope

Assignment: Do we learn more from finding out that we have made mistakes or from our successful actions? Plan your response, and then write an essay...


Prompt: “What man calls civilization always results in deserts. Man is never on the square – he uses up the fat and greenery of the earth. Each generation wastes a little more of the future with greed and lust for riches.” Don Marquis

Assignment: With our modern awareness of ecology are we likely to make sufficient progress in conservation, or are we still in danger of damaging the earth beyond repair? Plan your response, and then write an essay...


Prompt: A man who waits to believe in action before acting is anything you like, but he is not a man of action. It is as if a tennis player before returning the ball stopped to think about his views of the physical and mental advantages of tennis. You must act as you breathe. Georges Clemenceau

Assignment: Is it true that acting quickly and instinctively is the best response to a crisis? Or are there times when an urgent situation requires a more careful consideration and a slower response? Plan your response, and then write an essay...


Prompt: There is usually a kernel of truth in the words Oscar Wilde puts in the mouth of his most outrageous characters – they wouldn’t be funny otherwise. One such gem that is worth pondering is: The only thing to do with good advice is to pass it on. It is never of any use to oneself.

Assignment: Is it true that when we most need advice we are least willing to listen to it? Or is good advice always welcome? Plan your response, and then write an essay...


Prompt: “Independence? That’s middle class blasphemy. We are all dependent on one another, every soul of us on earth.” Bernard Shaw expected to provoke controversy with these words, but I would agree with him that these days there is too much emphasis on independence. While it is certainly true that excessive dependence on others is not a sign of maturity, total independence of others is neither attainable nor desirable: we need to be mature, and unselfish enough to recognize our interdependence.

Assignment: Do we put too much emphasis on self-reliance and independence, and are we afraid of admitting that we need other people in our lives? Plan your response, and then write an essay...



In fact, you know what... you gave me a terrific idea. I will steal it from you and credit you as well. I'll get to it after my conference. Thank you. John Muradeli · 2 years ago

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@John Muradeli These are actually quite decent essay topics. I hadn't read the Clemenceau quote before; definitely food for thought, and action. And as for any credit, if your "terrific idea" pans out then yeah, I'm all for it. :) Brian Charlesworth · 2 years ago

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@John Muradeli I still remember the essay section of the SAT I took back in 1966--"The problem with having an open mind is that sometimes your brains fall out. Express in your essay your views on this." In retrospect, my submitted essay was simply too stuffy and appallingly boring with pedantic analyses. Today, I would have had a lot more fun with it, the hell with what the examiner would have thought of it. As long as the spelling and grammar was correct, with no incomplete sentences, like this one. Michael Mendrin · 2 years ago

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@Michael Mendrin Haha. How had I never heard that "open mind" quote before? Apparently I've been hiding under a rock on Mars all these years. Anyway, It appears to have an interesting origin story as well. Brian Charlesworth · 2 years ago

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@Michael Mendrin GO AHEAD PLEASE!

...unless you want me to beat you to it with my version of HARD. ;)

(P.S. - what's Y!A? Yahoo answers?) John Muradeli · 2 years, 3 months ago

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@John Muradeli Yes Michael Mendrin · 2 years, 3 months ago

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@Michael Mendrin No harm in posting it, probably as a "note" rather than a "problem". That way there could be more of a discussion about how to approach the question, rather than people just getting frustrated that they can't solve it. I'm curious to see which problem you considered to be the hardest on Y!A.

His solutions could be cryptic, and often came out of left field .... no, make that left field in a different ballpark. I occasionally revisit them, (and yours), for inspiration. Brian Charlesworth · 2 years, 3 months ago

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@Brian Charlesworth Bah.. terminology and crap. Darn do I wanna chime in and discuss the definition of intelligence and all that, but I've so totally gotta take care of my 7APs! And I still gotta get back to that meaning of life posts and all! Aghh...

I'll get back to this. Sooner or later. You'll see...

But just shortly, I'd consider Mr. Mendrin's level of intelligence genius. And I can justify (BUT NOT NOW!) this claim. But the type of genius I'd assign would not necessarily be a type everyone expects. And not to say, it will be purely a weak speculation, and extrapolation at best.

You can never tell exactly, or even reasonably approximately about a person's intellect over the web. Especially not on a website that just focuses on math and physics... Lol.

Oh look, I already typed so much. better get outa here.

BYEH! John Muradeli · 2 years, 3 months ago

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@John Muradeli I don't doubt that genius exists and is a valid "label" we can assign to someone, but its definition is nebulous at best. IQ isn't much of an indicator: Feynman's was 125 and no one doubts his status as a genius. For me, I would make that judgement based on a visceral reaction, i.e., I would need to be "blown away" by someone's ideas, thought processes, actions, presence, etc.. Godel and Einstein do that for me, but so do Picasso, James Joyce, Jorge Luis Borges and even athletes like Michael Jordan, Wayne Gretzky and Roger Federer. Perhaps the label is assigned by consensus; if enough of us agree, then so be it.

And yes, it's impossible to make such an assessment over the web, but if your gut is saying "yes", then who am I to question. :) Continuing good luck with your APs. Brian Charlesworth · 2 years, 3 months ago

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Hey! But what is the relation of the picture in this?? Anuj Shikarkhane · 2 years, 5 months ago

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@Anuj Shikarkhane Amj, it's art. A very pretty picture of a very complicated (but hugely impractical) formula that actually cranks out prime numbers. You put it up on a wall or on a T-shirt, and say, "hey, that looks cool", and that's as far it'll ever go. See my response to Cody Johnson here. Michael Mendrin · 2 years, 5 months ago

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@Michael Mendrin Can you explain how this works? Agnishom Chattopadhyay · 2 years, 3 months ago

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@Michael Mendrin Can this formula generate all the primes?(starting from 2 to the largest prime found till now??) Aneesh Kundu · 2 years, 5 months ago

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@Aneesh Kundu Yes, it can. In theory. But it takes ridiculously long computer times just to be able to work out very small primes. Michael Mendrin · 2 years, 5 months ago

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Waaw your problems are mindblowing i am your big fan Aman Sharma · 2 years, 5 months ago

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By any chance do u teach math??? Aneesh Kundu · 2 years, 5 months ago

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@Aneesh Kundu No, I've never held any teaching position. Michael Mendrin · 2 years, 5 months ago

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I have a question for you about calculus and analysis in general, how do you solve problems rapidly ? do you rely on your experience and use techniques that you already used or you treat each problem independently ? Haroun Meghaichi · 2 years, 5 months ago

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@Haroun Meghaichi Eh, about that, Haroun. I know that Brilliant is designed to help students excel in tests and math Olympiads, which means you're supposed to be solve problems with a pencil and paper. But I've been using Mathematica for decades now, as part of my work and other things, so I use it. Remember, I'm 64 now, I don't need to take tests any more. So I prefer to work on problems that you can't just plug into Mathematica and get the answer. Because, really, otherwise I'm not learning much, aren't I? But I will say that I often use Mathematica to check on other people's problems to make sure their "correct answers" actually are, and help get them fixed if need be. Michael Mendrin · 2 years, 5 months ago

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@Michael Mendrin I use computers too for more intricate problems. I write python programs to search for solutions once I figured out the theory. Steven Zheng · 2 years, 5 months ago

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@Steven Zheng Seconded on using Wolfram / Java / Python / etc. to solve problems, once you've understood the theory. I'm sure multiple threads already exist on the subject, but the test mantra of forcing students to solve problems without access to all the technologies they will have in a real work environment is just... old, and out of touch. I'm not even sure that letting them use the internet much of the time is even a bad idea - those who can, and wish to learn, will still do so even with access to the internet, and those who don't wish to learn will still find ways to try to circumvent the system. I have no shame for using automated tools to solve problems I see here, even if it trivializes the work a bit, because at the end, I'm still able to get the same answer as the others. Daniel Ploch · 2 years, 5 months ago

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@Daniel Ploch I can tell you that if you have a job to do and people expect results, you don't get points for just using a pencil and paper. You go and use a computer and whatever resources you can muster. There are plenty of really difficult problems where computers are a must, and still hard to do even with computers.

NASA's Saturn V Rocketdyne F-1 rocket engine (still the most powerful ever built) was engineered using slide rules. They don't use slide rules any more. Michael Mendrin · 2 years, 5 months ago

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@Daniel Ploch Yeah. Who likes row reducing matrices or calculating eigenvalues by hand? Steven Zheng · 2 years, 5 months ago

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@Steven Zheng Amen, bro Michael Mendrin · 2 years, 5 months ago

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I used to think I was rather profound at maths until I read your problems recently. Honestly, they are far beyond my understanding. (Haven't learnt calculus. Still have about three years till they teach that...)

Do you have any advice in learning mathematics? Tan Wee Kean · 2 years, 5 months ago

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@Tan Wee Kean The best way to learn mathematics is to read, think and discuss. Being on Brilliant is a good way, but you should read mathematics books about more advanced topic that you can still understand (don't go to the forbidden section yet). Try to create your own math problems once you learn something new. Then share it with others. Make sure you ask a lot of questions too! Steven Zheng · 2 years, 5 months ago

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You are now 64 but still you are quite fit and hasn't experienced the signs of old age - dementia, Alzheimer's etc.

Are you still working? What were you in your young age? What has been your inspiration? How are you able to keep up with your love for maths still?

I have many more questions and I will surely ask you later. Kartik Sharma · 2 years, 5 months ago

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@Kartik Sharma My mother is a lot older than me, and she still doesn't show signs either. I think she's going to outlive me.

Yes, I'm still working, and I hope to someday able to help farmers in central California deal with the recurrent droughts with improved irrigation practices (this actually involves some engineering). I have no idea why I got so interested in math when I was tot. I still remember my 5th grade teacher who decided to try teaching his class concepts of solid geometry and volumes using formulas. It just blew me away. Ever since then, it's always been on my mind. Some people chew gum constantly. This is my mental gum. Michael Mendrin · 2 years, 5 months ago

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@Michael Mendrin Great!! I hope your dream comes true! And your memory is quite good, you remember your 5th grade teacher!! :) Yes, your 'gum' dialogue, like it!!

BTW, can I ask one more question? What do you think is intelligence? and What do you think is Mathematics?

*Sorry, but they are 2 questions!! ;) Kartik Sharma · 2 years, 5 months ago

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@Kartik Sharma Those are really profound questions, there's too much to be said for both. But certainly, the two are related! Michael Mendrin · 2 years, 5 months ago

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@Michael Mendrin Are you an engineer? Thaddeus Abiy · 2 years, 5 months ago

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@Thaddeus Abiy A long time ago I passed the examinations to qualify for a structural engineer license, but was not able to spare the time to work 2 years full-time for a licensed structural engineer, which is a State of California requirement. But I've been a licensed California general contractor for a long time, and I did engineering calculations as part of design---and then passed them on to a licensed structural engineer to sign them off. Michael Mendrin · 2 years, 5 months ago

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Comment deleted Sep 16, 2014

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@Vighnesh Raut My father, who also had structural engineering skills, had always been a "by the book" guy. He'd buy me a math or mechanics book, and I would start in the middle and jump around, and maybe eventually get to the beginning of the book. He always got mad at me for that. Well, at least my way of doing things is to always try to "see the big picture", and then work downwards towards the details. When tackling a complicated problem, first I start with a toy version of it. to get a feel for it, and then go back to the problem. Now, but getting the big picture often does means looking ahead and glancing over the entire book, so you know what to expect, and how things sort of hang together, before tackling the details and the first pages and problems. I don't buy that idea that you must be shielded from material later in the book "before you're ready for it". I don't think your mind really works best that way. Michael Mendrin · 2 years, 5 months ago

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